Step 1: Open the Case and Examine the Circuit Board
Beginning from the right side and moving to the left, you see the battery leads from the switches and the red "on" LED. One of the resistors limits the current to the LED. The other provides the correct bias current to the transistor (the black object at the lower right corner of the circuit board). Transformers cannot work with direct current. The transistor switches on and off rapidly to create a rising and falling voltage for the transformer to step up. Next comes the transformer. My friend's unit has only one capacitor for storage of the charge while it builds up to the maximum charge of the capacitor. This unit has two capacitors and four diodes. I did not check it out thoroughly, but I believe the diodes and the capacitors make a voltage multiplier. At the far left of the circuit board are four bleeder resistors to dissipate the charge on the capacitors when one is finished using the swatter. The bare wires are the high voltage wires to the grid wires in the yellow swatter frame.
Step 2: What I Found
Sometimes you can check a transistor while it is in the circuit by using the diode check function on your meter. You are looking for current to flow in one direction between two legs, but not in the other. My friend's transistor blocked all current in both directions. That was further confirmation the transistor was defective.
While this one has numbers on the face that can help to identify a replacement, there were none on my friend's transistor. NPN transistors are more common than PNP. I guessed these circuits use a low voltage NPN switching transistor, like a 2N2222. These are very common and available at Radio Shack on a blister pack.
Step 3: Replace the Transistor
Always use a heat sink when soldering the leads of semiconductors, like transistors. They can easily be ruined by too much heat.
When I finished soldering the transistor leads, I made sure the solder joints looked good. Then I put the circuit board back into the swatter frame and closed it up. (On the one shown here, the battery leads broke and had to be soldered back in place at the battery holder and one of the switches.) When I put the batteries in and pressed the switches, I rested a screwdriver on one of the grid wires and moved it near to the next grid wire. A large spark leaped from the next grid wire to the tip of screwdriver.
The transistor is the most likely component to fail in a circuit like this. Also check any diodes. I believe my friend's new swatter failed when tested at the factory. A high voltage wire was too close to part of the low voltage circuit. High voltage probably flowed back to the transistor and blew it to pieces.
Update: (September 15, 2009) The fly swatter shown in these pictures became weak in its output and then stopped working altogether. The transistor seemed to test good, but when I replaced it the LED lit again. Still, there was no spark when resting a screwdriver on one grid wire and moving it toward the next grid wire. I checked the capacitors and diodes. All seem to be good. I took ohmmeter readings on the transformer windings. The secondary read 268 ohms, but the secondary windings on an identical working unit showed 423 ohms. I am suspicious the secondary winding of the transformer has a short between its windings. Findings a replacement transformer at a reasonable price is not likely. I will probably buy a replacement fly swatter.